Abstract:
We consider a smooth groupoid of the form Σ⋊Γ, where Σ is a Riemann surface and Γ a discrete pseudogroup acting on Σ by local conformal diffeomorphisms. After defining a K-cycle on the crossed product C 0(Σ)⋊Γ generalising the classical Dolbeault complex, we compute its Chern character in cyclic cohomology, using the index theorem of Connes and Moscovici. This involves in particular a generalisation of the Euler class constructed from the modular automorphism group of the von Neumann algebra L ∞(Σ)⋊Γ.
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Received: 1 February 2000 / Accepted: 3 December 2000
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Perrot, D. A Riemann–Roch Theorem¶for One-Dimensional Complex Groupoids. Commun. Math. Phys. 218, 373–391 (2001). https://doi.org/10.1007/s002200100404
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DOI: https://doi.org/10.1007/s002200100404